What does big oh notation have to do with asymptotes?

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- Jan 14th 2012, 04:56 PMJskidrelation between asymptotes and big oh notation
What does big oh notation have to do with asymptotes?

- Jan 14th 2012, 07:50 PMCaptainBlackRe: relation between asymptotes and big oh notation
- Jan 14th 2012, 08:37 PMJskidRe: relation between asymptotes and big oh notation
- Jan 14th 2012, 09:48 PMCaptainBlackRe: relation between asymptotes and big oh notation
- Jan 15th 2012, 09:37 AMemakarovRe: relation between asymptotes and big oh notation
- Jan 15th 2012, 11:00 AMJskidRe: relation between asymptotes and big oh notation
- Jan 15th 2012, 11:02 AMemakarovRe: relation between asymptotes and big oh notation
- Jan 15th 2012, 11:11 AMJskidRe: relation between asymptotes and big oh notation
- Jan 15th 2012, 11:18 AMemakarovRe: relation between asymptotes and big oh notation
According to Wikipedia, asymptote is a straight line. Therefore, neither $\displaystyle x^2$ nor $\displaystyle x^3$ can be an asymptote. Yes, it is possible that f(x) is an asymptote to g(x) but g(x) is not an asymptote to f(x) because (the graph of) f(x) is a straight line and g(x) is not. But the fact that f(x) = O(g(x)) does not imply that either f(x) or g(x) is an asymptote to anything or that that either f(x) or g(x) has an asymptote.

- Jan 15th 2012, 11:27 AMJskidRe: relation between asymptotes and big oh notation
- Jan 15th 2012, 11:43 AMemakarovRe: relation between asymptotes and big oh notation
An asymptote is a straight line by definition.

Edit: It may happen that f(x) is an asymptote to g(x) for some f(x) and g(x). This implies that f(x) is a straight line. This does not imply that g(x) is a straight line; therefore, this does not imply that g(x) is an asymptote to anything. - Jan 15th 2012, 11:46 AMJskidRe: relation between asymptotes and big oh notation
- Jan 15th 2012, 11:54 AMemakarovRe: relation between asymptotes and big oh notation
Well, f(x) is not a family of functions; it's one function. You may consider O(g(x)) as a family, but not f(x). Second, why would you think that f(x) = O(g(x)) is somehow related to f(x) greater than or equal to g(x)? If anything, the first, very rough, idea behind f(x) = O(g(x)) is that f(x) <= g(x). (In reality, f(x) <= C * g(x) for some constant C, and this inequality has to hold only eventually.)

- Jan 15th 2012, 11:55 AMJskidRe: relation between asymptotes and big oh notation
Here f(n) is O(g(n))

http://img440.imageshack.us/img440/1410/helpbv.png

but I see no asymptote? - Jan 15th 2012, 12:01 PMemakarovRe: relation between asymptotes and big oh notation